Supervisory Control of Fuzzy Discrete Event Systems Under Partial Observation

Supervisory control of fuzzy discrete event systems (FDES) under partial observation is investigated in this article. Without loss of generality, we consider FDES with constraints where a FDES is modeled by a fuzzy automaton. Sequences of events that can be generated by the system are regarded as constraints and are modeled by a crisp automaton. A supervisor is designed to control the FDES so that the supervised system is prevented from entering a prespecified set of illegal/unsafe fuzzy states. A necessary and sufficient condition for the existence of a supervisor is obtained. When the condition is satisfied, an online supervisor can be designed. Fuzzy state estimation problem is first solved, as the supervisor is fuzzy-state-estimate-based. A method is developed to estimate fuzzy state iteratively after observation of each new event. We show that the supervisor so developed ensures the safety of the system and is least restrictive among all possible safe supervisors. Potential of the theoretical results for real-world applications is illustrated through an example of HIV/AIDS treatment decision-making.